As Congress bids farewell to three of the dominant Republicans of recent decades, it ought to pay attention — deep attention, not a nod of the head — to what made them remarkable.

Former Rep. Henry Hyde (Ill.), who died last week, retiring former Speaker Dennis Hastert (Ill.) and retiring former Senate Majority Leader Trent Lott (Miss.) all had in common an abiding dedication to the institution of Congress, a priority of passing legislation over merely playing politics and an ability to work across party lines that earned them praise from colleagues on both sides of the aisle.

Hastert, the longest-serving Republican Speaker in history, said in his farewell address to the House in November: “I continue to worry about the breakdown of civility in our political discourse. I tried my best, but I wish I had been more successful.”

We wish he had been, too. Hastert himself — the bear-like, soft-spoken ex-wrestling coach — was a soothing figure at the helm of the GOP and of the House from 1999 through 2006. He also stoutly defended the institution of Congress against an administration of his own party when it conducted an unprecedented FBI raid on the office of Rep. William Jefferson (D-La.).

Unfortunately, as Rutgers University professor Ross Baker told National Public Radio, Hastert “will go down in history as Tom DeLay’s [R-Texas] front man,” referring to the ultra-partisan former House Majority Leader. Along with DeLay, Hastert imposed a rule that bills would not be brought up for passage unless they had majority support from majority Republicans, thereby cutting Democrats out of any important role in the legislative process.

It was Trent Lott’s gift to be both a staunch conservative and still able to overcome partisan rancor to bypass filibusters and pass legislation with bipartisan support — working with the Clinton administration, for instance, to pass welfare reform, clean water, health care portability and minimum-wage legislation.

Lott suffered a huge personal blow in being ousted from the majority leadership after making ill-considered remarks about the late segregationist Sen. Strom Thurmond (R-S.C.), but he vindicated himself among colleagues by being elected this year as Minority Whip.

Lott’s retirement only one year into his current term was greeted with cynicism about his presumed intent to become a lobbyist, but he deserves credit for serving 35 years in Congress when other Members departed far sooner for K Street millions.

Of the three, Hyde most of all combined the traits of a conviction politician — especially fighting abortion, but also the worldwide AIDS epidemic — with the ability to gain almost universal affection and respect. He took a leading part in one of the most polarizing episodes in recent history — Clinton’s impeachment — yet his was a career that embodied the ideals that Hastert urged upon his colleagues in his farewell address.

“We each have a responsibility to be passionate about our beliefs. That is healthy government,” Hastert said. “But we also have a responsibility to be civil, to be open-minded and to be fair — to listen to one another.” He was applauded, naturally. But his message — and Hyde’s and Lott’s careers — deserve to be lived up to.